How hard is it to control an election?

Abstract

Some voting schemes that are in principle susceptible to control are nevertheless resistant in practice due to excessive computational costs; others are vulnerable. We illustrate this in detail for plurality voting and for Condorcet voting.

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

“…Campaign management comprises all sorts of activities for influencing the outcome of an election, including well-known scenarios such as bribery (Faliszewski, Hemaspaandra, & Hemaspaandra, 2009;Dorn & Schlotter, 2012;Schlotter, Elkind, & Faliszewski, 2011;Elkind, Faliszewski, & Slinko, 2012) and control (Bartholdi III, Tovey, & Trick, 1992;Elkind, Faliszewski, & Slinko, 2011;Erdélyi, Piras, & Rothe, 2011). While these works relate to campaigning in case of classical voting scenarios where one typically wants to make a specific candidate win or to prevent him from winning, Christian, Fellows, Rosamond, and Slinko (2007) introduced the scenario of lobbying in multiple referenda.…”

Elections with Few Candidates: Prices, Weights, and Covering Problems

“…WMM is NP-hard even for the case of a single element in the universe. 2 There is a name clash between the literature on covering problems and that on elections. In the former, "weights" refer to what voting literature would call "prices."…”

“…Definition 1 (Bartholdi et al [2], Faliszewski et al [12,21]). In each of the problems Approval-$BRIBERY (priced bribery), Approval-$CCAV (priced control by adding voters), and Approval-$CCDV (priced control by deleting voters), we are given an approval election E = (C, V ) with C = {p, c 1 , .…”

“…and we ask whether a group of manipulators can cast votes to ensure their preferred candidate's victory), election control problems [2,17] (where we are given an election and ask if we can ensure a given candidate's victory by adding/deleting candidates/voters), or bribery [10,12,24] and campaign management problems [3,5,8,23] (where we want to ensure a given candidate's victory by changing some of the votes, but where each vote change comes at a price and we are bound by a budget). We focus on the case where we have a few candidates but (possibly) many voters.…”

Voting on Actions with Uncertain Outcomes

“…This paradox is closely related to Arrow's independence of irrelevant alternatives [2]: Arrow postulated that for any reasonable form of preference aggregation the relative collective ranking of two alternatives should only depend on their relative rankings provided by the individuals, and not on any third ("irrelevant") alternative. Our example demonstrates that the Borda rule, when used as an aggregator for preference orders, violates this desideratum: the relative ranking of A and B adopted by the collective does depend on C. Our paradox also has close connections to the topic of election control by means of adding (or deleting) candidates, widely studied in computational social choice [4,9], which in turn relies on violations of Arrow's independence axiom: our example demonstrates how adding candidate C to a Borda election in which B was winning can result in A becoming the new winner.…”